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Unformatted text preview: Homework 4 solutions Section 4.2 1. Auxiliary equation is r 2 + 5 r + 6 = ( r + 2)( r + 3) = 0. y h = C 1 e 2 t + C 2 e 3 t 2. Auxiliary equation is r 2 r 2 = ( r 2)( r + 1) = 0. y h = C 1 e 2 t + C 2 e t 3. Auxiliary equation is r 2 + 8 r + 16 = ( r + 4)( r + 4) = 0. y h = C 1 e 4 t + C 2 te 4 t 4. Auxiliary equation is r 2 + 6 r + 9 = ( r + 3)( r + 3) = 0. y h = C 1 e 3 t + C 2 te 3 t 5. Auxiliary equation is r 2 + r 1 = 0, r = 1 ± √ 5 2 . y h = C 1 e 1+ √ 5 2 t + C 2 e 1 √ 5 2 t 6. Auxiliary equation is r 2 5 r + 6 = ( r 2)( r 3) = 0, y h = C 1 e 2 t + C 2 e 3 t 7. Auxiliary equation is 2 r 2 + 7 r 4 = 0, r = 1 / 2 , 4. y h = C 1 e t/ 2 + C 2 e 4 t 8. Auxiliary equation is 6 r 2 + r 2 = 0, r = 1 ± √ 49 12 = 2 3 , 1 2 . y h = C 1 e 2 t/ 3 + C 2 e t/ 2 9. Auxiliary equation is r 2 r 11 = 0, r = 1 ± √ 45 2 = 1 ± 3 √ 5 2 . y h = C 1 e 1+3 √ 5 2 t + C 2 e 1 3 √ 5 2 t 10. Auxiliary equation is 4 r 2 4 r + 1 = (2 r 1)(2 r 1) = 0. y h = C 1 e t/ 2 + C 2 te t/ 2 11. Auxiliary equation is 4 r 2 + 20 r + 25 = (2 r + 5)(2 r + 5) = 0. y h = C 1 e 5 t/ 2 + C 2 te 5 t/ 2 12. Auxiliary equation is 3 r 2 + 11 r 7 = 0. r = 11 ± √ 205 6 y h = C 1 e 11+ √ 205 6 t + C 2 e 11 √ 205 6 t 14. The auxiliary equation is r 2 + r = r ( r + 1) = 0, y h = C 1 + C 2 e t (Note that...
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This note was uploaded on 04/10/2008 for the course PHYS 141 taught by Professor Dienes during the Spring '08 term at Arizona.
 Spring '08
 Dienes
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